Question

14. When conducting a large sample test of $\mathrm{H}_0: p=p_0$ for a single proportion, the test statistic is $z=\frac{\left(\hat{p}-p_0\right)}{\sqrt{\frac{p_0\left(1-p_0\right)}{n}}}$, where $\hat{p}$ is the sample proportion. Which of the following best explains the justification for the denominator of this test statistic?
(A) The standard deviation of $\hat{p}$ is known when the null hypothesis is true.
(B) The standard deviation of $\hat{p}$ is known when the alternative hypothesis is true.
(C) The sample size is large and therefore the standard deviation of $p_0$ is approximated well.
(D) The standard deviation of $p_0$ is known when the null hypothesis is true.
(E) The standard deviation of $p_0$ is known when the alternative hypothesis is true.